The theory of operation of a laser beam amplification device is reviewed briefly below. The latter is illustrated in FIG. 1a. It mainly comprises a laser beam amplifying crystal 1 and optical pumping laser beams 3. The beams 3 inject optical energy into the amplifying crystal. The laser source originating the pumping beams is not shown in the figure. Then, the laser beam to be amplified 2 passes through the crystal of the amplifier a number of times by means of mirror-based optical devices 21. On each pass, it extracts a portion of the energy injected in the pumping and is thus amplified in the crystal. Generally, the number of passes is between 2 and 8, as long as the energy contributed by the pumping beams 3 is not totally extracted by the laser beam 2. Thus, the extraction of the energy contributed by the pumping beams 3 is improved.
In this type of laser beam amplification device configuration, a spurious phenomenon known as transverse lasing appears between the deposition of energy in the crystal by optical pumping and its extraction by the beam to be amplified. This phenomenon is linked to the creation in the crystal of a laser subcavity along an axis transversal to the pumping axis, that is, between two areas of the surface linking the input and output faces of the crystal: it greatly affects the efficiency of the amplification device. The transverse lasing occurs between areas of the crystal when the oscillation condition of the duly created subcavity is satisfied, that is, when there is conservation of the energy on a round trip from the centre C to the edge, as illustrated in FIG. 1b. 
This means that the transverse lasing appears between two areas of the surface or the circumference linking the input and output faces of the crystal when: GT.R>1.
GT being the transverse gain of the crystal, and R being the reflection coefficient at an interface separating the circumference of the crystal from the outside.
Conventionally, R is:
  R  =            [                        Δ          ⁢                                          ⁢          n                          ∑          n                    ]        2  with                Δn: difference in optical indices between the crystal and the outside        Σn: sum of the optical indices of the crystal and of the outside.        
In practice, the transverse lasing appears for GT.R>0.2 and firstly on the faces of the crystal that are exposed to the pumping which present the greatest gain, that is, those that absorb most of the pumping energy.
The current techniques for combating the transverse lasing consist in minimizing the reflection coefficient R. They are based on the use of materials with matched index as external coating for the crystal. The duly created index matching limits the reflections at the edge of the crystal and prevents the appearance of transverse lasing.
However, as described previously, the crystal receives high pumping energy. This induces in the crystal thermal effects which impair the efficiency of the amplification device. These crystals must therefore be cooled.
However, the index matching materials used to combat the transverse lasing present the following defect. They are poor conductors of heat and cooling of the crystal is impaired.